Statistical Relationship between Quantitative and Dichotomous Variables: Student’s Test and Moving Average Approach

Document Type : Original Article


1 Federal state budgetary institution of science "Institute of Industrial Ecology" Ural Branch of the Russian Academy of Sciences

2 Institute of Industrial Ecology, Ural Branch of the Russian Academy of Sciences


A new technique is proposed for evaluating the statistical relationship between a quantitative variable Y and a dichotomous variable X assuming two values: X=0 and X=1. The technique is based on the division of the quantitative variable Y into strata by the moving average technique and computation of average values in the strata for the variables Y and X. Stratification turns the dichotomous variable X into a quantitative one. Once the variable X has been transformed in this way, the statistical relationship between Y and X may be analyzed by linear regression and by analysis of variance. Thus, the technique proposed expands the range of methods available for analyzing statistical relationships between quantitative and dichotomous variables. Specific examples are used to compare the moving average technique with the t-test for symmetric (normal) and asymmetric distributions of quantitative variable Y. It is shown that the statistical relationship between stratified Y and X can be strongly different for a symmetrically (normally) distributed variable Y.


Main Subjects

Articles in Press, Accepted Manuscript
Available Online from 15 September 2023
  • Receive Date: 28 March 2023
  • Revise Date: 22 June 2023
  • Accept Date: 15 September 2023